* Weaker yen underpinned shares in September
* Investors warily watch Japanese political developments
TOKYO, Sept 29 (Reuters) - Japan's Nikkei share average edged down on Friday but was on track for a solid monthly gain, buoyed by a weaker yen.
The Nikkei was down 0.3 percent at 20,305.04 points at the end of morning trading.
It was up marginally on the week, but posted a solid 3.4 percent rise in September. It rose 1.4 percent in the quarter, taking its gain so far in 2017 to 6.2 percent.
"Month-end is having an impact here, and I don't think you should be interpreting too much into the market being down today," said Stefan Worrall, director of Japan equity sales at Credit Suisse in Tokyo.
"The domestic focus may be adding to some caution at the end of the month, and the end of the quarter," he said.
Upbeat economic data early on Friday underpinned sentiment and kept losses in check.
Japan's core inflation picked up in August, though it remained well below the central bnak's target, industrial output rose more than expected and demand for labour remained at its strongest in over 40 years in a further sign of solid momentum in the world's third-largest economy.
A weaker yen also gave Japanese stocks a tailwind in September. The dollar gained 2.5 percent against the yen in the month.
Investors were wary of political developments ahead of a snap lower house election called by Japanese Prime Minister Shinzo Abe, who was apparently calculating that it would consolidate another term for his Liberal Democratic Party-led coalition even if it reduced its lower house dominance to a simple majority.
But a fledgling party led by popular Tokyo governor Yuriko Koike was gaining momentum ahead of the Oct. 22 election, as the biggest opposition Democratic Party said on Thursday that it would step aside to let its candidates run under her conservative, reformist banner.
Genki Sushi Co jumped 5.8 percent. The owner of the restaurant chain will buy a one-third stake in bigger rival Sushiro Global Holdings Ltd from private equity firm Permira, a person with direct knowledge of the deal said. Sushiro shares rose 4.6 percent.
Toshiba Corp's shares gained 2.6 percent, after it said on Thursday that it had signed an $18 billion deal to sell its chip unit to a consortium led by Bain Capital LP, overcoming a key hurdle as it scrambles for funds to stave off a potential delisting.
Japan's Tokyo Electron Device Ltd shares rose 5.2 percent after scaling their highest peak since October 2007, after the company hiked its group forecasts.
Shares of Koito Manufacturing Co fell 6.2 percent, after the company trimmed its full-year group outlook.
Japan's Kose Corp shares were 2.5 percent higher. The cosmetics company is on track to post about a 40 percent jump in its April-September operating profit, to around 26 billion yen ($230.93 million), Nikkei reported.
The broader Topix was down 0.3 percent at 1,670.76, while the JPX-Nikkei Index 400 was 0.3 percent lower at 14,754.55. (Reporting by Lisa Twaronite; Editing by Kim Coghill)